\begin{array}{l}
\text {Q1. Draw rough diagrams to illustrate the following: } \\
\text {(i) Open curve } \quad \quad \text {(ii) Closed curve }
\end{array}\begin{array}{l}
\text {Sol. (i) Open curve is a curve in which the beginning and the end points does not cut each other or are different.} \\
\end{array}\begin{array}{l}
\text {(ii) Closed curve ia a curve in which the beginning and the end points are the same and cuts each other.} \\
\end{array}\begin{array}{l}
\text {Q2. Classify the following curves as open or closed:} \\ \\
\end{array}\begin{array}{l}
\text {Sol. } \\\text {Definitions :} \\
\text {Open curve is a curve in which the beginning and the end points does not cut each other or are different.} \\
\text {Closed curve ia a curve in which the beginning and the end points are the same and cuts each other.} \\\text {(i) Open curve } \\
\text {(ii) Closed curve } \\
\text {(iii) Closed curve } \\
\text {(iv) Open curve } \\
\text {(v) Open curve } \\
\text {(vi) Closed curve } \\
\end{array}\begin{array}{l}
\text {Q3. Draw a polygon and shade its interior. Also draw its diagonals, if any.}
\end{array}\begin{array}{l}
\text {Sol. } \\
\text {Here is the required with diagonals and with its interior shaded.} \\
\end{array}\begin{array}{l}
\text {Q4. Illustrate, if possible, each one of the following with a rough diagram: } \\
\text {(i) A closed curve that is not a polygon. } \\
\text {(ii) An open curve made up entirely of line segments. } \\
\text {(iii) A polygon with two sides. } \\
\end{array}\begin{array}{l}
\text {Sol. } \\
\text {(i) A closed curve that is not a polygon.} \\
\end{array}\begin{array}{l}
\text {(ii) An open curve made up entirely of line segments.} \\
\end{array}\begin{array}{l}
\text {(iii) Not possible because polygons are closed figures.} \\
\end{array}
\begin{array}{l}
\text {Q5. Following are some figures: Classify each of these figures on the basis of the following } \\
\text {(i) Simple curve } \quad \text {(ii) Simple closed curve } \quad \text {(iii) Polygon } \\
\text {(iv) Convex polygon } \quad \text {(v) Concave polygon } \quad \text {(vi) Not a curve } \\
\end{array}\begin{array}{l}
\text {Sol. } \\
\text {(i) It is a simple closed curve and a concave polygon. } \\
\text {(ii) It is a simple closed curve and a convex polygon. } \\
\text {(iii) It is not a curve; hence, it is not a polygon. } \\
\text {(iv) It is not a curve; hence, it is not a polygon. } \\
\text {(v) It is a simple closed curve but not a polygon. } \\
\text {(vi) It is a simple closed curve but not a polygon. } \\
\text {(vii) It is a simple closed curve but not a polygon. } \\
\text {(viii) It is a simple closed curve but not a polygon. } \\
\end{array}
\begin{array}{l}
\text {Q 6. How many diagonals does each of the following have? } \\
\text {(i) A convex quadrilateral } \\
\text {(ii) A regular hexagon } \\
\text {(iii) A triangle }
\end{array}
\begin{array}{l}
\text {Sol. An n-sided convex polygon has } \frac {n(n – 3)}{2} \text { diagonals.} \\
\text {(i) A quadrilateral has } \frac {4(4 – 3)}{2} = 2 \text { diagonals.} \\
\end{array}\begin{array}{l}
\text {(ii) A regular hexagon has } \frac {6(6 – 3)}{2} = 9 \text { diagonals.} \\
\end{array}\begin{array}{l}
\text {(iii) A quadrilateral has } \frac {3(3 – 3)}{2} = 0 \text { diagonals.} \\
\Rightarrow \quad \text{A triangle has no diagonals.} \\
\end{array}\begin{array}{l}
\text {Q7. What is a regular polygon? State the name of a regular polygon of } \\
\text {(i) 3 sides } \\
\text {(ii) 4 sides } \\
\text {(iii) 6 sides }
\end{array}\begin{array}{l}
\text {Sol. } \\
\text {Definition : A regular polygon is an enclosed figure wholse all sides } \\
\text { and all angles are equal and. In a regular polygon minimum sides are three. } \\
\text {(i) 3 sides : A regular polygon with 3 sides is known as Equilateral triangle. } \\ \\
\text {(ii) 4 sides : A regular polygon with 4 sides is known as Rhombus. } \\ \\
\text {(iii) 6 sides : A regular polygon with 6 sides is known as Regular hexagon. }
\end{array}
